ĐK: \(x\le2\)
pt <=> \(2=2-x+\sqrt{2-x}\sqrt{3-x}+\sqrt{3-x}\sqrt{5-x}+\sqrt{5-x}\sqrt{2-x}.\)
<=> \(2=\sqrt{2-x}\left(\sqrt{2-x}+\sqrt{3-x}\right)+\sqrt{5-x}\left(\sqrt{2-x}+\sqrt{3-x}\right).\)
<=> \(2=\left(\sqrt{2-x}+\sqrt{3-x}\right)\left(\sqrt{5-x}+\sqrt{2-x}\right).\)
<=> \(2\left(\sqrt{5-x}-\sqrt{2-x}\right)=3\left(\sqrt{2-x}+\sqrt{3-x}\right)\)( vì \(\sqrt{5-x}-\sqrt{2-x}\ne0;\forall x\inℝ\))
<=> \(2\sqrt{5-x}=5\sqrt{2-x}+3\sqrt{3-x}\)
<=> \(4\left(5-x\right)=25\left(2-x\right)+9\left(3-x\right)+30\sqrt{\left(2-x\right)\left(3-x\right)}\)
<=> \(-57+30x=30\sqrt{\left(2-x\right)\left(3-x\right)}\)
<=> \(\hept{\begin{cases}30x-57\ge0\\900x^2-3420x+3249=900x^2-4500x+5400\end{cases}}\)
<=> \(\hept{\begin{cases}x\ge\frac{57}{30}\\x=\frac{239}{120}\end{cases}}\Leftrightarrow x=\frac{239}{120}\)tmđk
